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x^2-460x+21000=0
a = 1; b = -460; c = +21000;
Δ = b2-4ac
Δ = -4602-4·1·21000
Δ = 127600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{127600}=\sqrt{400*319}=\sqrt{400}*\sqrt{319}=20\sqrt{319}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-460)-20\sqrt{319}}{2*1}=\frac{460-20\sqrt{319}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-460)+20\sqrt{319}}{2*1}=\frac{460+20\sqrt{319}}{2} $
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